in the imputation stage, with \(p(Y|\varphi )\)  the marginal likelihood in (REF ). If we did carry out Bayesian inference in this way, we would use the same model, \(p(Y|\varphi ,\theta )\) , in both \(\pi (\varphi \mid Y, Z)\)  (imputation) and \(\pi (\theta \mid Y, \varphi )\)  (analysis). This is an imputation scheme [1]} calls “congenial”, where it is appropriate for the imputation and analysis to be carried out using the same model. In Cut-model inference the imputation and analysis use different models for \(\varphi \) , as \(p(Y|\varphi ,\theta )\)  is not used in the imputation. This may help in what [1]} calls “uncongenial” problems.
